The left end of a massless stick with length $l$ is placed on the corner of a table,as shown in the figure. $A$ point mass $m$ is attached to the center of the stick,which is initially held horizontal. It is then released. Immediately afterward,what normal force does the table exert on the stick?

Two small balls are fixed at the ends of a light rigid rod of length $L = 0.4 \ m$. The system is released from a height $h = 5 \ m$ with the rod horizontal. The balls collide with the horizontal surface and rebound. The coefficient of restitution between ball $A$ and the ground is $e_A = 0.6$ and that between ball $B$ and the ground is $e_B = 0.4$. Find the angular speed (in $rad/s$) of the rod just after the collision. Take the acceleration due to gravity $g = 10 \ m/s^2$.

The moment of inertia of a solid flywheel about its axis is $0.1\,kg\cdot m^2$. $A$ tangential force of $2\,kg\cdot wt$ is applied around the circumference of the flywheel with the help of a string and mass arrangement as shown in the figure. If the radius of the wheel is $0.1\,m$,find the angular acceleration of the solid flywheel (in $rad/s^2$). (Take $g = 9.8\,m/s^2$)

$A$ rigid body rotates about a fixed axis with variable angular velocity equal to $\alpha - \beta t$,where $t$ is time and $\alpha, \beta$ are constants. Find the angle (in radians) through which it rotates before it stops.

$A$ mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder,then with what acceleration will the mass be released? (Assume $g =$ acceleration due to gravity)

$A$ uniform rod of mass $m$ and length $l$ rotates in a horizontal plane with an angular velocity $\omega$ about a vertical axis passing through one end. The tension in the rod at a distance $x$ from the axis is